Novel Heavy-Traffic Regimes for Large-Scale Service Systems

DOI10.1137/140960815zbMath1322.60193arXiv1411.5251OpenAlexW2170159748MaRDI QIDQ5264993

Johan S. H. van Leeuwaarden, Britt Mathijsen, Augustus J. E. M. Janssen

Publication date: 21 July 2015

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.5251

zbMATH Keywords

Riemann zeta functionwaiting timesasymptotic analysiscentral limit theoremqueueing theorysaddle point methodGaussian random walkheavy-traffic regimeslarge service systems

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20)

Related Items (7)

Transient error approximation in a Lévy queue ⋮ MAD Dispersion Measure Makes Extremal Queue Analysis Simple ⋮ Spitzer's identity for discrete random walks ⋮ Dominant poles and tail asymptotics in the critical Gaussian many-sources regime ⋮ Heavy-traffic single-server queues and the transform method ⋮ Robust heavy-traffic approximations for service systems facing overdispersed demand ⋮ Pollaczek contour integrals for the fixed-cycle traffic-light queue

Uses Software

• DLMF

Cites Work

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